Resource pooling in congested networks: proportional fairness and product form

We review two areas of recent research linking proportional fairness with product form networks. The areas concern, respectively, the heavy traffic and the large deviations limiting regimes for the stationary distribution of a flow model, where the flow model is a stochastic process representing the randomly varying number of document transfers present in a network sharing capacity according to the proportional fairness criterion. In these two regimes we postulate the limiting form of the stationary distribution, by comparison with several variants of the fairness criterion. We outline how product form results can help provide insight into the performance consequences of resource pooling.     

Fusion multiplicities as polytope volumes: -point and higher-genus su(2) fusion

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess–Zumino–Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point ( ) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein–Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.     

Hydrogen bond formation to cyclic and acyclic polyethers

Equilibrium constants and enthalpies of hydrogen-bond formation of mcresol to various cyclic (crown) and acyclic polyethers have been determined in benzene solvent. Equilibrium constants indicated no evidence for an operative macrocyclic effect; the relationship between the increasing size of the equilibrium constant and the number of ether oxygens was rationalized with a simple statistical thermodynamic model. Enthalpies of interactions ranged between –19 and –23 kJ-mol^–1. In agreement with PCILO calculations, enthalpies of interaction were essentially independent of the number of oxygen atoms in the ether; no significant difference in enthalpies of interaction between cyclic and acyclic ethers was found.     

A Statewide Implementation of the Critical Features of Professional Development: Impact on Teacher Outcomes

This study is focused on a statewide implementation of the core conceptual framework for effective professional development in the United States. and associated impact on teacher quality and attitudes. The framework included content focus, active learning, coherence, duration, and collective participation. There were 252 participants in the study, who were involved in one of the five science or six mathematics programs. Findings indicated a significant impact on teacher quality for all participating programs. Teacher attitudes were positive at the baseline, and remained positive with some improvement at the end of the program. However, teacher perceived preparedness increased significantly across the duration of the program. Discussion of the findings and implications for professional development programs internationally are shared.     

Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies

The main purpose of this study is to establish the existence of a weak solution to the anti-plane stress problem on V-notch domains for a class of recently proposed new models that could describe elastic materials in which the stress can increase unboundedly while the strain yet remains small. We shall also investigate the qualitative properties of the solution that is established. Although the equations governing the deformation that are being considered share certain similarities with the minimal surface problem, the boundary conditions and the presence of an additional model parameter that appears in the equation and its specific range makes the problem, as well as the result, different from those associated with the minimal surface problem.     

Solution-phase counterion effects in supramolecular and mechanostereochemical systems

The self-assembly of molecular components into complex superstructures involves the subtle interplay of various noncovalent forces. Charged species are often utilised in self-assembly processes as a result of the favorable π-π, cation-π, electrostatic, and hydrogen bonding interactions that form between these species. Although the counterions associated with these charged species can exert significant effects on the synthesis, stability, and operation of superstructures in solution, rarely are the counterions considered, leading to misinterpretations and misunderstandings of the studied systems. In this tutorial review, we discuss a variety of solution-phase counterion effects, from the fundamental origins to innovative ways in which these effects are exploited for useful functions.     

A scaleable formal total synthesis of dehydrogliotoxin

A formal total synthesis of the epidithiodiketopiperazine natural product, dehydrogliotoxin (2), utilizing an intramolecular ring closure to form key intermediate 5 is described.     

In vitro evolution of ligands to the membrane protein caveolin

Membrane proteins comprise a third of the human genome, yet present challenging targets for reverse chemical genetics. For example, although implicated in numerous diseases including multiple myeloma, the membrane protein caveolin-1 appears to offer a poor target for the discovery of synthetic ligands due to its largely unknown structure and insolubility. To break this impasse and identify new classes of caveolae controlling lead compounds, we applied phage-based, reverse chemical genetics for the discovery of caveolin-1 ligands derived from the anti-HIV therapeutic T20. Substitution of homologous residues into the T20 sequence used a process analogous to medicinal chemistry for the affinity maturation to bind caveolin. The resultant caveolin-1 ligands bound with >1000-fold higher affinity than wild-type T20. Two types of ELISAs and isothermal titration calorimetry (ITC) measurements demonstrated high affinity binding to caveolin by the T20 variants with K(d) values in the 150 nM range. Microscopy experiments with the highest affinity caveolin ligands confirmed colocalization of the ligands with endogenous caveolin in NIH 3T3 cells. The results establish the foundation for targeting caveolin and caveolae formation in living cells.     

Catalytic oxidative cleavage of olefins promoted by osmium tetroxide and hydrogen peroxide

Hydrogen peroxide was employed as the terminal oxidant in the osmium tetroxide mediated oxidative cleavage of olefins, producing the corresponding aldehyde and ketone products. Aryl olefins are cleaved in good to excellent yield regardless of arene electronics. Alkyl olefins cleave in moderate to good yield for di- and tri-substituted alkenes.